Gyroscope

ABSTRACT

A gyroscope for sensing rate on at least two axes includes a substantially planar vibratory resonator having a ring or hoop like shape, carrier mode drive means for causing the resonator to vibrate in a Cos n 1 θ in-plane carrier mode where n 1  has an integer value of 2 or more. The gyroscope also includes support means for flexibly supporting the resonator, carrier mode pick off means for sensing in-plane movement of the resonator, X axis response mode pick off means for sensing out-of-plane Cos nθ response mode movement of the resonator in response to rotation of the gyroscope around the X axis, where n has a value of n 1 +1 or n 1 −1, and Y axis response mode pick off means for sensing out-of-plane Sin nθ response mode movement of the resonator in response to rotation of the gyroscope about the Y axis where n has a value n 1 +1 or n 1 −1, identical to that for the X axis response mode.

RELATED APPLICATION

This application is a continuation of International Application No.PCT/GB99/00722 filed, Mar. 10, 1999.

BACKGROUND OF THE INVENTION

This invention relates to a gyroscope suitable sensing rate on at leasttwo axes, and preferably on three axes.

Vibrating structure gyroscopes may be fabricated using a variety ofdifferent structures as the resonant element. These include beams,tuning forks, cylinders, hemispherical shells and rings. Successfulcommercial exploitation is dependent upon optimising the deviceperformance while minimising the cost. An additional goal for someapplications is reducing the size of the device.

Some conventional vibrating structure gyro designs are suitable forfabrication using modern micro-machining techniques. These may beconstructed from bulk Silicon, polysilicon or electro-formed metal.These fabrication methods provide the capability of producing miniaturegyros in high volume and at reduced cost.

Many applications for gyroscopic devices require rate sensitivity aboutall three axes. Conventional vibrating structure gyros provide singleaxis rate sensitivity and therefore three devices are required whichmust be aligned along orthogonal axes. A vibrating structure gyroincorporating a resonator design which is inherently capable of sensingaround three axes simultaneously would therefore be of great benefit. Asingle device would thus replace three conventional single axis unitswith obvious cost benefits. Also, the process of mounting and aligningthe three single axis gyros would not be required.

There is thus a need for an improved gyroscope which can sense rate onat least two axes.

SUMMARY OF THE INVENTION

According to a first aspect of the present invention there is provided agyroscope for sensing rate on at least two axes, including asubstantially planar vibratory resonator having a substantially ring orhoop-like shape structure with inner and outer peripheries extendingaround a common axis, carrier mode drive means for causing the resonatorto vibrate in a Cos n₁θ in-plane carrier mode, where n₁ has an integervalue of 2 or more, support means for flexibly supporting the resonatorand for allowing the resonator to vibrate, in response to the carriermode drive means, relative to the support means, carrier mode pick-offmeans for sensing in-plane movement of the resonator, X axis responsemode pick-off means for sensing out-of-plane Cos nθ response modemovement of the resonator in respect to rotation of the gyroscope aroundthe X axis, where n has a value of n₁+1 or n₁−1, and Y axis responsemode pick off means for sensing out-of-plane Sin nθ response modemovement of the resonator in respect to rotation of the gyroscope aboutthe Y axis, where n has a value of n₁+1 or n₁−1, identical to that forthe X axis response mode.

Preferably, the gyroscope includes X axis response mode drive means fornulling the X axis response mode movement of the resonator to permit thegyroscope to be operated in a forced feedback configuration.

Conveniently, the gyroscope includes Y axis response mode drive meansfor nulling the Y axis response mode movement of the resonator to permitthe gyroscope to be operated in a forced feed back configuration.

Advantageously, for sensing rate about two axes the support meansincludes a plurality of flexible legs flexibly connecting the resonatorto a support, with the number of legs N_(T) being given by N_(T)=4 n andwith the angular separation between the legs being given by 360°/N_(T).

Preferably, for sensing rate about three axes the gyroscope includes Zaxis response mode pick off means for sensing in-plane Sin n₁θ responsemode movement of the resonator in respect to rotation of the gyroscopearound the Z axis, where n₁ has an integer value of 2 or more, identicalto that for the in-plane carrier mode.

Conveniently, the gyroscope for sensing rate about three awes includes Zaxis response mode drive means for nulling the Z axis response modemovement of the resonator to permit the gyroscope to be operated in aforced feedback configuration.

Advantageously, the support means includes a plurality of flexible legsflexibly connecting the resonator to a support, with the number of legsN_(T) being given by N_(T)=4 nn₁ and with the angular separation betweenthe legs being given by 360°/N_(T).

Preferably, in a gyroscope of the present invention for sensing rateabout two axes the carrier mode is an in-plane Cos 2 θ mode, with thecarrier mode drive means including two drive elements, for initiatingthe carrier mode motion, located at 0° and 180° with respect to a fixedreference axis in the plane of the resonator, with the carrier mode pickoff means including two pick off elements, for detecting the carriermode motion, located at 90° and 270° with respect to the fixed referenceaxis, wherein the X axis response mode is a Cos 3 θ mode, with the Xaxis pick off means including three pick off elements located at 0°,120°, and 240° with respect to the fixed reference axis, with the X axisdrive means including three drive elements located at 60°, 180° and 300°with respect to the fixed reference axis, and wherein the Y axisresponse mode is a Sin 3 θ mode, with the Y axis pick off meansincluding three pick off elements located at 30°, 150° and 270° withrespect to the fixed reference axis and with the Y axis drive meansincluding three drive elements located at 90°, 210° and 330° withrespect to the fixed reference axis, which X and Y axis drive and pickoff elements are operable to detect and nullify the response modemotions.

Alternatively, the carrier mode is an in-plane Cos 3 θ mode, with thecarrier mode drive means including three drive elements located at 0°,120° and 240° with respect to a fixed reference axis in the plane of theresonator, with the carrier mode pick off means including three pick offelements located at 60°, 180° and 300° with respect to the fixedreference axis, wherein the X axis response mode is a Cos 2 θ mode, withthe X axis pick off means including two pick off elements located at 0°and 180° with respect to the fixed reference axis, with the X axis drivemeans including two drive elements located at 90° and 270° with respectto the fixed reference axis, and wherein the Y axis response mode is aSin 2 θ mode, with the Y axis pick off means including two pick offelements located at 45° and 225° with respect to the fixed referenceaxis and with the Y axis drive means including two drive elementslocated at 135° and 315° with respect to the fixed reference axis.

Conveniently, the carrier mode is an in-plane Cos 3 θ mode, with thecarrier mode drive means including three drive elements located at 0°,120° and 240° with respect to a fixed reference axis in the plane of theresonator, with the carrier mode pick off means including three pick offelements located at 60°, 180° and 300° with respect to the fixedreference axis, wherein the X axis response mode is a Cos 4 θ mode, withthe X axis pick off means including four pick off elements located at0°, 90°, 180° and 270° with respect to the fixed reference axis, withthe X axis drive means including four drive elements located at 45°,135°, 225° and 315° with respect to the fixed reference axis and whereinthe Y axis response mode is a Sin 4 θ mode, with the Y axis pick offmeans including four pick off elements located at 22.5°, 112.5° and292.5° with respect to the fixed reference axis, and with the Y axisdrive means including four drive elements located at 67.5°, 157.5°,247.5° and 337.5° with respect to the fixed reference axis.

Advantageously, a gyroscope for sensing rate of three axes, includes Zaxis response mode pick off means for sensing in-plane Sin 2 θ responsemode movement of the resonator, which Z axis pick off means includes twopick off elements located at 45° and 225° with respect to the fixedreference axis, and including Z axis response mode drive means havingtwo drive elements located at 135° and 315° with respect to the fixedreference axis.

Preferably, a gyroscope for sensing rate on three axes, includes Z axisresponse mode pick off means for sensing in-plane Sin 3 θ response modemovement of the resonator, which Z axis pick off means includes threepick off elements located at 90°, 210° and 330° with respect to thefixed reference axis, and including Z axis response mode drive meanshaving three drive elements located at 30°, 150° and 270° with respectto the fixed reference axis.

Advantageously, the resonator is made from metal, quartz, polysilicon orbulk silicon.

Advantageously the drive means and the pick off means are electrostatic,electromagnetic, piezoelectric or optical.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the present invention, and to show how thesame may be carried into effect, reference will now be made, by way ofexample, to the accompanying drawings in which:

FIG. 1a is a schematic diagram of a vibrating structure gyroscope notaccording to the present invention;

FIG. 1b shows the three orthogonal axes along which the velocity,rotation and force vectors lie with the structure of FIG. 1a;

FIGS. 2a and 2 b show graphically the shapes of mode pairs exhibitingCos n₁θ and Sin n₁θ radial displacements for n₁=2;

FIGS. 3a and 3 b are graphical shapes similar to those of FIGS. 2a and 2b for n=3;

FIGS. 4a and 4 b are graphical shapes similar to those of FIGS. 2a and 2b and FIGS. 3a and 3 b but for n₁=4;

FIGS. 5a and 5 b are graphical representations on three axes for theforce components generated by a rotation of a gyroscope according to thepresent invention about the Y axis; for a Cos 2 θ in-plane carrier mode.

FIGS. 6a and 6 b are similar graphical representations to those of FIGS.5a and 5 b but representing rotation about the X axis;

FIGS. 7a and 7 b are graphical representations on three axes of thevibration mode shapes exhibiting Cos nθ and Sin nθ out-of-planedisplacements for n=1;

FIGS. 8a and 8 b are graphical representations similar to those of FIGS.7a and 7 b but for n=2;

FIGS. 9a and 9 b are graphical representations similar to those of FIGS.8a and 8 b but for n=3;

FIGS. 10a and 10 b are graphical representations similar to those ofFIGS. 9a and 9 b but for n=4;

FIG. 11a shows in plan view a diagrammatic example of a resonator andsupport legs suitable for use in a gyroscope according to the presentinvention;

FIG. 11b shows in plan view a further resonator and support legstructure for use with a gyroscope according to the present invention;

FIG. 12 is a schematic diagram in plan view of part of a gyroscopeaccording to a first embodiment of the present invention showing driveand pick off elements;

FIG. 13 is a cross sectional view on a diagonal of the structure of FIG.12 showing additional detail;

FIG. 14 is a schematic plan view of part of a gyroscope according to asecond embodiment of the present invention;

FIG. 15 is a diagrammatic plan view of part of a gyroscope according toa third embodiment of the present invention;

FIG. 16 is a diagrammatic plan view of part of a gyroscope according toa fourth embodiment of the present invention;

FIG. 17 is a diagrammatic plan view of part of a gyroscope according toa fifth embodiment of the present invention and;

FIG. 18 is a diagrammatic plan view of part of a gyroscope according toa sixth embodiment of the present invention.

DETAILED DESCRIPTION

A common feature of all conventional vibrating structure gyro designs isthat they maintain a resonant carrier mode oscillation. This providesthe linear momentum which produces the Coriolis force F_(c), when thegyro is rotated around the appropriate axis. The magnitude of this forceis given by:

F_(c)=2 Ω mv  (1)

where Ω is the applied rate, m is the mass and v the linear velocity.The velocity, rotation and force vectors lie along mutually orthogonalaxes as shown in FIGS. 1a and 1 b of the accompanying drawings.

One of the simplest implementations for a vibrating structure gyro is abeam 1 shown in FIG. 1a. The carrier mode vibration is a bending motionin the xz-plane as shown in FIGS. 1a and 1 b. A rotation applied aboutthe axis of the beam 1 (z-axis) will generate Coriolis forces which setthe beam 1 into motion in the yz-plane, at the carrier frequency. Theamplitude of motion in this axis will be proportional to the appliedrotation rate. The sensitivity of such a device may be enhanced bydesigning the structure such that the Coriolis force directly excites aresonant mode. The amplitude of motion is then amplified by the Q of theresponse mode. For a simple beam made of isotropic material this will beachieved using a beam of square cross-section where the X and Ydimensions are matched.

A rotation about the Y-axis will also induce Coriolis forces in the beam1. These will act along the length of the beam (z-axis). The beam isextremely stiff in this direction and is therefore insensitive to theseforces. However this simple linear vibration along a single axis is ableto respond to rotations around two axes. Implementation of a practicalgyroscope based on these responses requires a resonator design thatenables these Coriolis force components to couple directly into responsemodes along the appropriate axes.

In order to produce a gyroscope capable of sensing rate along three axesthe carrier mode motio must contain velocity components along twoorthogonal axes. The structure must also be designed such that theCoriolis forces induced as a result of rotation about each axis coupleinto response modes whose resonant frequency may be matched to that ofthe carrier. Planar ring structures utilising Cos n₁θ in-plane carriermodes where θ is the angular location around the ring circumferencerelative to a fixed datum and n₁ has a fixed integer value of 2 or more,are particularly suited to this application. The n₁=1 mode is not asuitable carrier as it is a rigid body translation of a ring resonatorand thus only has velocity components along a single axis.

For perfect ring resonator structures the Cos n₁θ in-plane vibrationmodes exist as degenerate pairs at a mutual angle of (90/n₁)°. The θ=0°reference axis R for the modal diagrams is along the Y-axis in thepositive direction. Using this fixed reference the lode pairs will haveshapes exhibiting Cos n₁θ and Sin n₁θ radial displacements. The modeshapes for n₁=2 are shown in FIGS. 2a and 2 b. The two extremes ofmaximum displacement from the unexcited ring position, during a singlevibration cycle, are shown for each mode of the air. The axes indicatethe displacement from the unexcited ring position for a ring of radius1.0 (arbitrary units). The modes exist at a mutual angle of 45°. Themode shapes for n₁=3 are similarly shown in FIGS. 3a and 3 b. Theseexist at a mutual angle of 30°. The corresponding shapes for the n₁=4modes are shown in FIGS. 4a and 4 b and exist at a mutual angle of22.5°.

Vibrating structure gyro designs using ring structures, capable ofsensing rate about a single axis, are well known. These use one of thein-plane Cos n₁θ/mode pair (typically n₁=2) as the carrier. A rotationabout the axis normal to the plane of the ring (z-axis) couples energyinto the second mode of the pair with the induced amplitude of motionbeing proportional to the applied rate.

Using these carrier modes, rotations about axes in the plane of the ringwill also give rise to Coriolis forces. These will act along the z-axisand will tend to set the ring into out-of-plane motion. The distributionof these forces will vary with angular position θ and, for rotationabout the Y-axis, Ω_(y), will be given by:

F_(c)(θ)=F_(n) _(i) ₊₁Ω_(y) Sin(n₁+1)θ+F_(n) ₁ ⁻¹Ω_(y) Sin(n₁−1)θ  (2)

The parameters Fn₁+1 and Fn₁−1 are constants which depend on the precisegeometry of the ring and the support means, the material and the valueof n₁. The out-of-plane Coriolis force thus has components which vary asSin(n₁+1)θ and Sin(n₁−1)θ. For the same carrier mode, a rotation aboutthe X-axis will induce Coriolis forces given by:

F_(c)(θ)=F_(n) ₁ ₊₁Ω_(x) Cos(n₁+1)θ+F_(n) ₁ ⁻¹Ωy Cos(n₁−1)θ  (3)

The out-of-plane Coriolis force in this instance has components varyingas Cos(n₁+1)θ and Cos(n₁−1)θ. By way of example, for the case where thecarrier is the Cos 2 θ in-plane mode shown in FIG. 2a, a rotation aboutthe Y-axis will generate force components which vary as Sin θ and sin 3θ. These are shown in FIGS. 5a and 5 b, respectively. A rotation aboutthe X-axis will generate components which vary as Cos θ and cos 3 θ.These are shown in FIGS. 6a and 6 b.

The z-axis displacement of the out-of-plane modes will also exhibit aCos nθ angular dependence and, like the in-plane modes these exist asdegenerate pairs at a mutual angle of (90/n)°. The mode shapes for n=1exist at a mutual angle of 90° (i.e. Sin θ and Cos θ radialdisplacements) and are shown in FIGS. 7a and 7 b. As with the previousmodal diagrams, the two extremes of motion are shown with the restposition of the ring indicated by the broken lines. The correspondingplots for the n=2, 3 and 4 modes are shown in FIGS. 8a, 8 b, 9 a, 9 b,10 a and 10 b.

The functional forms of the Coriolis force components shown in FIGS. 5aand 6 a precisely match those of the n=1 out-of-plane mode shown inFIGS. 7a and 7 b. Similarly, the forms of the Coriolis force componentsshown in FIGS. 5b and 6 b precisely match those of the n=3 out-of-planemodes shown in FIGS. 9a and 9 b. Clearly these modes may be directlyexcited as a result of the rotation induced Coriolis forces.

Examination of equations 2 and 3 indicates that any Cos n₁θ in-planecarrier mode can couple into Cos(n₁+1)θ, Sin(n₁+1)θ, Cos(n₁−1) andSin(n₁−1)θ out-of-plane modes when rotated around the appropriate axis.To be of practical use in any gyro configuration, the amplitude ofmotion generated must be as large as possible to maximise the gyrosensitivity. This is achieved by matching the mode frequencies of thecarrier and a chosen pair out-of-plane response modes. The resultantmotion is thus amplified by the Q of the response mode vibration. Thein-plane mode frequencies are not affected by changing the depth (iez-axis dimension) of the ring. The out-of-plane mode frequencies aredirectly sensitive to this parameter and may therefore be independentlyadjusted. By judicious control of the dimensions of the ring resonatorand support structure it is possible to match the Cos n₁θ in-planecarrier frequency with either the Cos(n₁+1)θ and Sin(n₁+1)θ or theCos(n₁−1)θ and Sin(n₁−1)θ out-of-plane modes. It is therefore possibleto design multi-axis gyro schemes using a variety of carrier andresponse mode combinations.

The Cos 2 θ carrier mode can couple into the Sin θ, Cos θ, Sin 3 θ andCos 3 θ out-of-plane response modes. These are shown in FIGS. 7a, 7 b, 9a and 9 b respectively. The use of the Cos 2 θ carrier in combinationwith the Sin 3 θ and Cos 3 θ response modes according to the presentinvention is capable of being implemented as a three axis rate sensor.

The resonator in a vibrating structure gyro preferably is substantiallyplanar having a ring or hoop like shape resonator structure 2 with innerand outer peripheries extending around a common axis A normal to a fixedreference axis R in the plane of the resonator structure 2, which axis Rextends in the direction of the Y axis. The ring structure is supportedby support means including a plurality of compliant support legs 3. Whendriven in a Cos 2 θ carrier mode both the ring and support legs are inmotion. However, the ring 2 is very stiff in comparison to the supportlegs 3 and the carrier frequency is predominantly set by the ringdimensions. This effectively isolates the resonator from the mountingand reduces environmental sensitivity.

The Sin θ and Cos θ out-of-plane modes (FIGS. 7a and 7 b) will involvesignificant deflection and stress in the support legs 3 withinsignificant distortion of the ring 2. Due to the compliance of thelegs this Cos θ mode naturally occurs at a significantly lower frequencythan the Cos 2 θ carrier. The Sin 3 θ and Cos 3 θ response modes (FIGS.9a and 9 b) distort and stress the ring significantly. Its natural modefrequency will therefore be significantly higher than that of the Cos θmode. The Cos 2 θ carrier and the Sin 3 θ and Cos 3 θ response modefrequencies may thus be matched with considerably less adjustment of theleg to ring stiffness ratio. This helps to maintain the environmentalcapability of the gyroscope.

When using the out-of-plane Cos θ response modes, the legs 3 will alwaystransmit a non-zero torque to the support structure as the ring 2 rocksabout the input rotation axis. In contrast, the out-of-plane Sin 3 θ andCos 3 θ response mode will not transmit any net reaction force to thesupport structure if an appropriate number of legs are used. This willbe true for all Cos nθ modes where n>1.

Practical gyroscopes of the present invention may be constructed usinghigher order in-plane carrier modes. The Cos 3 θ in-plane mode (FIG. 3b)may be used as the carrier in conjunction with either the Cos 2 θ andSin 2 θ or the Cos 4 θ and Sin 4 θ out-of-plane response modes. Theseresponse modes are shown in FIGS. 8a, 8 b, 10 a and 10 b respectively.The Cos 4 θ carrier (FIG. 4a) will couple into the Sin 3 θ, Cos 3 θ, Sin5 θ and Cos 5 θ response modes. Corresponding combinations of higherorder are also feasible. In practice, however, the higher order modecombinations become increasingly onerous to implement. The mode shapesbecome progressively more complex and require a larger number ofdiscrete drive and pick off elements to excite and sense the vibrations.Also, the support legs 3 act as point spring masses which perturb themode frequencies. The number and location of these legs need to bematched to the mode symmetry to avoid induced splitting of thedegenerate mode frequencies. The number of legs required increasesrapidly with the mode order thus rendering some designs impractical on asmall size gyroscope.

A three axis gyroscope according to the present invention may beconstructed by using a combination of Sin 2 θ and Cos 2 θ in-plane andthe Sin 3 θ and Cos 3 θ out-of-plane modes. This gyroscope requires thefrequencies of four modes to be matched (one carrier plus three responsemodes). However, for a perfectly symmetric ring 2 of uniform thickness,the Sin 2 θ and Cos 2 θ mode pair will have identical frequencies.Similarly, the Sin 3 θ and Cos 3 θ mode pair will also be matched.Therefore, due to the high degree of symmetry, the design of theresonator dimensions is, in practice, reduced to an exercise in matchingonly two frequencies (ie those of the two degenerate mode pairs). Forthe dimensions commonly used in ring resonators designed for single axisoperation the Cos 3 θ out-of-plane and Cos 2 θ carrier mode frequenciesnaturally occur relatively closely matched in frequency. Adjusting thedepth (z-axis dimension) of the ring does not alter the in-planefrequencies. It does, however, have a distinct affect of theout-of-plane frequencies. Matching the Sin 2 θ, Cos 2 θ, Sin 3 θ and Cos3 θ mode frequencies may therefore be achieved by appropriate adjustmentof a single ring dimension.

In terms of the mode dynamics, the support legs 3 appear as point springmasses acting at the point of attachment which differentially perturbthe mode frequencies. In order to prevent frequency splitting andmaintain the positional indeterminacy of the modes, the number andlocation of the legs must be matched to the mode symmetry. For any Sinn₁θ and Cos n₁θ mode pair this necessitates the use of 4 n₁equi-angularly spaced legs (where n₁ is 2 or more). The Sin 2 θ and Cos2 θ in-plane modes therefore require 8 equally spaced legs. The Sin 3 θand Cos 3 θ out-of-plane modes require 12 legs to maintain theirindeterminacy. To satisfy this requirement simultaneously for both modepairs implies the use of 24 legs equally spaced at 150 intervals aroundthe ring 2. This number is the lowest common multiple of the in-planeand out-of-plane leg numbers and may be derived for any three axis gyromode combination from the following expression:

Number of legs N_(T)=n×n₁×4  (4)

The angular spacing of these legs is given by [360/N_(T)]°.

For planar ring resonator structures the support legs 3 are designedsuch that the modal behaviour is dominated by the ring characteristics.This requires the legs to be radially and tangentially compliant, incomparison to the ring itself. Many design variations are possible whichachieve these requirements. FIGS. 11a and 11 b show two possibilitiesfor the twenty-four support leg structure of one embodiment of thepresent invention. These designs are consistent with the use of largernumbers of support legs 3.

Vibrating structure gyroscopes of the invention may be constructed usingstandard fabrication and machining techniques. They are also suitablefor fabrication using micro-machining techniques. The principle ofoperation and drive and pick off orientations will be identicalregardless of the fabrication route. The resonator may be constructedfrom any material possessing suitable mechanical properties includingmetal, quartz, polysilicon or bulk silicon. The ring 2 may be driveninto oscillation using a variety of drive means. These includeelectrostatic, electromagnetic, piezo or optical means. The amplitude ofmotion may similarly be detected using electrostatic, electromagnetic,piezo or optical pick off means.

The preferred three axis gyroscope embodiment uses electrostatic driveand pick off means. The orientation of drive and pick off elements forthis embodiment is shown in FIG. 12. The location of the ring 2 isindicated by the dashed lines. The in-plane Cos 2 θ carrier mode isdriven into oscillation using drive elements 4 whose effective centresare located at 0° and 180° around the outer periphery of the ring 2 withrespect to the fixed reference axis R. For each element, the surfacenormal to the plane of the ring 2 facing the ring circumference formsone plate of the capacitor with the facing segment of the ringcircumference forming the other plate. The ring 2 is maintained at afixed potential with respect to the drive elements 4. An oscillatingvoltage applied to the drive element plates at the carrier modefrequency will generate an electrostatic force setting the ring 2 intooscillation. Pick off elements 5, for the carrier mode located at 90°and 270° with respect to the fixed reference axis R, similarly formcapacitors with the facing ring segments and are used to detect themotion of the ring 2 as the capacitor gap varies. Pick off elements 6located at 45° and 225° with respect to the axis R detect the amplitudeof the in-plane Sin 2 θ response mode when the gyroscope is rotatedaround the z-axis. Z axis drive elements 7 located at 135° and 315° withrespect to the axis R, may be used to null the mode movement to allowthe gyroscope to operate in a forced feedback configuration. Whenoperated in this mode the nulling drive is proportional to the appliedrate. This mode of operation provides performance advantages over theopen loop mode.

The Cos 3 θ out-of-plane response mode providing the X-axis ratesensitivity will have anti-nodes at 0°, 60°, 120°, 180°, 240° and 300°locations, with respect to the axis R, around the ring circumference.The sin 3 θ Y-axis response mode will have anti-nodes at 30°, 90°, 150°,210°, 270° and 330° with respect to the axis R. Drive and pick offelements may be located at any appropriate combinations adjacent tothese points. Conveniently, twelve plate like elements are positioneddirectly under the rim to form capacitors between said plates and theparallel facing segments of the bottom surface of the ring.Conveniently, the plates should extend beyond the inner and outer edgesof the ring rim. The in-plane motion of the carrier mode will nottherefore change the effective plate area and will not be inadvertentlydetected by these plate like elements. Elements 8 located at 0°, 120°and 240° are used as X-axis pick off elements. The signals from theseelements will be in phase and may be conveniently summed together togive enhanced sensitivity in detecting the mode movement. Plate likeelements 9 located at 60°, 180° and 300° with respect to the axis R areused as drive elements with the same drive voltage being applied to allthese elements to null the motion to facilitate force feedbackoperation. Similarly, plate like elements 10 located at 30°, 150° and270° with respect to the axis R are the Y-axis pick off elements withplate like elements 11 located at 90°, 210° and 330°, with respect tothe axis R forming the drive elements for that mode.

FIG. 13 shows a cross-section view through the centre of the resonatorring 2 along the Y-axis showing additional detail of the devicearchitecture. The X and Y axis drive and pick off elements areconductive sites laid onto the surface of an electrically insulatingsubstrate layer 12. These element sites are connected via tracks to bondpads (not shown) which can be electrically connected to the controlcircuitry. The ring 2 is attached, via the support legs 3, to a centralsupport pedestal 13. This pedestal extends beneath the ring 2 andattaches rigidly to the substrate layer 12 such that the ring andsupport legs are freely suspended above the substrate layer. Thein-plane mode drives and pick off elements are rigidly attached to thesubstrate 12 with tracking and bond pads provided as require to enableconnection to the control circuitry.

Modifications to this structure are possible. The addition of a secondinsulating substrate layer rigidly fixed above the resonator ring 2,duplicating the out-of-plane drive and pick off element capacitor platearray, would enhance the sensitivity of the gyroscope along the X and Yaxes. This would, however, complicate the fabrication process and wouldnot alter the essential design features or functionality of thegyroscope.

A two axis gyroscope according to the present invention may befabricated using the same Cos 2 θ in-plane carrier mode and Sin 3 θ andCos 3 θ out-of-plane response modes. For this embodiment the resonatordesign is such that the in-plane Sin 2 θ and Cos 2 θ mode frequenciesare deliberately separated. Advantageously, this frequency split willfix the carrier mode position at a known angular location which may bealigned to the carrier mode drive and pick off means. The carrier modefrequency must still be matched to that of the out-of-plane responsemodes. If twelve support legs 3 are used then the symmetry of the Cos 3θ modes is maintained. This will, however, generate a splitting of thein-plane Sin 2 θ and Cos 2 θ modes and thus fix the mode positions asrequired. Generally, for two axis gyroscope operation the requirednumber of support legs is given by the following expression:

Number of legs N_(T)=n×4  (5)

The angular spacing is [360/N_(T)]°.

This implementation will provide rate sensitivity about the X and Y axesonly. The in-plane response mode drive and pick off means are thus notrequired. FIG. 14 shows a schematic of the gyroscope layout for thisembodiment. This is essentially the same as the three axis embodiment ofFIGS. 12 and 13, with the exception of the absence of the Z axisin-plane response mode drive elements 7 and pick off elements 6 and thedifferent number of support legs, and hence like reference numerals havebeen used. No further description will therefore be given.

A two or three axis gyroscope may be fabricated using Sin 3 θ and Cos 3θ in-plane modes in conjunction with sin 2 θ and Cos 2 θ out-of-planeresponse modes. For the three axis embodiment the degeneracy of both thein-plane sin 3 θ and Cos 3 θ and out-of-plane Sin 2 θ and Cos 2 θ modepairs must be maintained. This dictates the use of twenty-four supportlegs 3 on the resonator ring 2. A schematic of the orientation of thedrive and pickoff elements is shown in FIG. 15. The topology of thegyroscope is largely identical to the previously described embodimentswith the exception of the drive and pick off element layout. The Cos 3 θin-plane carrier drive means elements 14 are located at 0°, 120° and240° with respect to the fixed reference axis R with the pick off meanselements 15 located at 60°, 180° and 300° with respect to the axis R.The Z axis sin 3 θ in-plane response mode drive elements 16 are locatedat 30°, 150° and 270° with respect to the axis R with the pick offelements 17 at 90°, 210° and 330° with respect to the axis R. Theout-of-plane Cos 2 θ X axis response mode pick off elements 18 arelocated at 0° and 180° with the nulling drive elements 19 at 90° and270° with respect to the axis R. The Y axis out-of-plane Sin 2 θ pickoff elements 20 are located at 45° and 225° with respect to the axis Rwith the nulling Y axis drive elements 21 at 135° and 315° with respectto the axis R.

The two axis embodiment of this Cos 3 θ in-plane carrier andout-of-plane Sin 2 θ and Cos 2 θ response mode combination requires thein-plane mode degeneracy to be lifted. This may be achieved by the useof eight support legs. Otherwise, this embodiment differs from the threeaxis one only in the omission of the in-plane response mode driveelements 16 and pick off elements 17. The drive and pick off meanslayout is shown in FIG. 16.

A two or three axis gyroscope of the invention may be fabricated using aSin 3 θ and Cos 3 θ in-plane and a Sin 4 θ and Cos 4 θ out-of-plane modecombination. The three axis embodiment requires the use of forty-eightsupport legs 3 to maintain all the appropriate mode symmetries. Thisembodiment is shown schematically in FIG. 17. The Cos 3 θ in-planecarrier mode drives 22 are located at 0°, 120° and 240° with respect tothe fixed reference axis R with the pick off elements 23 at 60°, 180°and 300° with respect to the axis R. The in-plane Z axis Sin 3 θresponse mode drive elements 24 are located at 30°, 150° and 270° withrespect to the axis R with the z axis Cos 3 θ mode in-plane pick offelements 25 at 90°, 210° and 300° with respect to the axis R.

The X axis Cos 4 θ out-of-plane response mode pick off elements 26 arelocated at 0°, 90°, 180° and 270° with respect to the fixed referenceaxis R, with X axis Cos 4 θ out-of-plane response mode nulling driveelements 27 at 45°, 135°, 225° and 315° with respect to the axis R. TheY axis Sin 4 θ out-of-plane response mode pick off elements 28 arelocated at 22.5°, 112.5°202.5° and 292.5° with respect to the axis Rwith Y axis Sin 4 θ out-of-plane response mode nulling drive elements 29at 67.5°, 157.5°, 247.5° and 337.5° with respect to the axis R.

The corresponding two axis gyroscope embodiment of the inventionrequires sixteen support legs 3. The layout for this embodiment, shownin FIG. 18, is otherwise identical to the three axis one of FIG. 17 withthe exception of the omission of the z axis in-plane response mode driveelements 24 and pick off elements 25. Like parts have been given likenumbers to those of FIG. 17 and will not be further described.

Two and three axis rate sensors may be fabricated using higher orderin-plane and out-of-plane mode combinations. These will requireprogressively higher numbers of support legs to maintain the necessarymode symmetries and a larger number of drive and pick off elements. As aresult of this these embodiments, while feasible, become progressivelymore complicated to fabricate, particularly in a small size gyroscope.

Additionally in a gyroscope of the invention for sensing rate about twoaxes, the resonator 2 and support means are dimensioned so that the Cosn₁θ in-plane carrier mode and Sin nθ and Cos nθ out-of-plane responsemode frequencies are matched, and for sensing rate about three axes thedimensions are such that the Cos n₁θ in-plane carrier mode, Sin n₁θin-plane response mode and Sin nθ and Cos nθ out-of-plane response modefrequencies are matched.

What is claimed is:
 1. A gyroscope for sensing rate on at least twoaxes, including a substantially planar vibratory resonator having asubstantially ring or hoop-like shape structure with inner and outerperipheries extending around a common axis, carrier mode drive means forcausing the resonator to vibrate in a Cos n₁θ in-plane carrier mode,where n₁ has an integer value of 2 or more, support means for flexiblysupporting the resonator and for allowing the resonator to vibrate, inresponse to the carrier mode drive means, relative to the support means,carrier mode pick-off means for sensing in-plane movement of theresonator, X axis response mode pick-off means for sensing out-of-planeCos nθ response mode movement of the resonator in respect to rotation ofthe gyroscope around the X axis, where n has a value of n₁+1 or n₁−1,and Y axis response mode pick off means for sensing out-of-plane Sin nθresponse mode movement of the resonator in respect to rotation of thegyroscope about the Y axis, where n has a value of n₁+1 or n₁−1,identical to that for the X axis response mode.
 2. A gyroscope accordingto claim 1, including X axis response mode drive means for nulling the Xaxis response mode movement of the resonator to permit the gyroscope tobe operated in a forced feedback configuration.
 3. A gyroscope accordingto claim 1, including Y axis response mode drive means for nulling the Yaxis response mode movement of the resonator to permit the gyroscope tobe operated in a forced feed back configuration.
 4. A gyroscopeaccording to claim 1, wherein for sensing rate about two axes thesupport means includes a plurality of flexible legs flexibly connectingthe resonator to a support, with the number of legs N_(T) being given byN_(T)=4 n and with the angular separation between the legs being givenby 360°/N_(T).
 5. A gyroscope according to claim 1, for sensing rateabout three axes, including Z axis response mode pick off means forsensing in-plane Sin n₁θ response mode movement of the resonator inrespect to rotation of the gyroscope around the Z axis, where n₁ has aninteger value of 2 or more, identical to that for the in-plane carriermode.
 6. A gyroscope according to claim 5, including Z axis responsemode drive means for nulling the Z axis response mode movement of theresonator to permit the gyroscope to be operated in a forced feedbackconfiguration.
 7. A gyroscope according to claim 5, wherein the supportmeans includes a plurality of flexible legs flexibly connecting theresonator to a support, with the number of legs N_(T) being given byN_(T)=4 nn₁ and with the angular separation between the legs being givenby 360°/N_(T).
 8. A gyroscope according to claim 2, for sensing rateabout two axes, wherein the carrier mode is an in-plane Cos 2 θ mode,with the carrier mode drive means including two drive elements, forinitiating the carrier mode motion, located at 0° and 180° with respectto a fixed reference axis in the plane of the resonator, with thecarrier mode pick off means including two pick off elements, fordetecting the carrier mode motion, located at 90° and 270° with respectto the fixed reference axis, wherein the X axis response mode is a Cos 3θ mode, with the X axis pick off means including three pick off elementslocated at 0°, 120°, and 240° with respect to the fixed reference axis,with the X axis drive means including three drive elements located at60°, 180° and 300° with respect to the fixed reference axis, and whereinthe Y axis response mode is a Sin 3 θ mode, with the Y axis pick offmeans including three pick off elements located at 30°, 150° and 270°with respect to the fixed reference axis and with the Y axis drive meansincluding three drive elements located at 90°, 210° and 330° withrespect to the fixed reference axis, which X and Y axis drive and pickoff elements are operable to detect and nullify the response modemotions.
 9. A gyroscope according to claim 2, wherein the carrier modeis an in-plane Cos 3 θ mode, with the carrier mode drive means includingthree drive elements located at 0°, 120° and 240° with respect to afixed reference axis in the plane of the resonator, with the carriermode pick off means including three pick off elements located at 60°,180° and 300° with respect to the fixed reference axis, wherein the Xaxis response mode is a Cos 2 θ mode, with the X axis pick off meansincluding two pick off elements located at 0° and 180° with respect tothe fixed reference axis, with the X axis drive means including twodrive elements located at 90° and 270° with respect to the fixedreference axis, and wherein the Y axis response mode is a Sin 2 θ mode,with the Y axis pick off means including two pick off elements locatedat 45° and 225° with respect to the fixed reference axis and with the Yaxis drive means including two drive elements located at 135° and 315°with respect to the fixed reference axis.
 10. A gyroscope according toclaim 2, wherein the carrier mode is an in-plane Cos 3 θ mode, with thecarrier mode drive means including three drive elements located at 0°,120° and 240° with respect to a fixed reference axis in the plane of theresonator, with the carrier mode pick off means including three pick offelements located at 60°, 180° and 300° with respect to the fixedreference axis, wherein the X axis response mode is a Cos 4 θ mode, withthe X axis pick off means including four pick off elements located at0°, 90°, 180° and 270° with respect to the fixed reference axis, withthe X axis drive means including four drive elements located at 45°,135°, 225° and 315° with respect to the fixed reference axis and whereinthe Y axis response mode is a Sin 4 θ mode, with the Y axis pick offmeans including four pick off elements located at 22.50, 112.5° and292.5° with respect to the fixed reference axis and with the Y axisdrive means including four drive elements located at 67.5°, 157.5°,247.5° and 337.5° with respect to the fixed reference axis.
 11. Agyroscope according to claim 8, for sensing rate of three axes, includeZ axis response mode pick off means for sensing in-plane Sin 2 θresponse mode movement of the resonator, which Z axis pick off meansincludes two pick off elements located at 45° and 225° with respect tothe fixed reference axis, and including Z axis response mode drive meanshaving two drive elements located at 135° and 315° with respect to thefixed reference axis.
 12. A gyroscope according to claim 9, for sensingrate on three axes, includes Z axis response mode pick off means forsensing in-plane Sin 3 θ response mode movement of the resonator, whichZ axis pick off means includes three pick off elements located at 90°,210° and 330° with respect to the fixed reference axis, and including Zaxis response mode drive means having three drive elements located at30°, 150° and 270° with respect to the fixed reference axis.
 13. Agyroscope according to claim 1, wherein the resonator is made from metalquartz, polysilicon or bulk silicon.
 14. A gyroscope according to claim2, including Y axis response mode drive means for nulling the Y axisresponse mode movement of the resonator to permit the gyroscope to beoperated in a forced feed back configuration.
 15. A gyroscope accordingto claim 2, wherein for sensing rate about two axes the support meansincludes a plurality of flexible legs flexibly connecting the resonatorto a support, with the number of legs N_(T) being given by N_(T)=4 n andwith the angular separation between the legs being given by 360°/N_(T).16. A gyroscope according to claim 3, wherein for sensing rate about twoaxes the support means includes a plurality of flexible legs flexiblyconnecting the resonator to a support, with the number of legs N_(T)being given by N_(T)=4 n and with the angular separation between thelegs being given by 360°/N_(T).
 17. A gyroscope according to claim 2 forsensing rate about three axes, including Z axis response mode pick offmeans for sensing in-plane Sin n₁θ response mode movement of theresonator in respect to rotation of the gyroscope around the Z axis,where n₁ has an integer value of 2 or more, identical to that for thein-plane carrier mode.
 18. A gyroscope according to claim 3 for sensingrate about three axes, including Z axis response mode pick off means forsensing in-plane Sin n₁θ response mode movement of the resonator inrespect to rotation of the gyroscope around the Z axis, where n₁ has aninteger value of 2 or more, identical to that for the in-plane carriermode.